Q&A #5978

Teachers' Lounge Discussion: Prime factorization using trees

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2003032310:18:24
Subject: Re: how do I figure out  prime factorization?

On 2003032307:23:21, Nyla wrote:
>Please help me figure out the prime factorization for a number like
>1713.I have trouble with big numbers.

To start, you only have to search for prime numbers less than the
square root of 1713.  

These prime numbers are: 2,3,5,7,11,13,17,19,23,29,31,37,41.  That
looks like a hard problem but usually it is easy.  
Since the number is odd, we can eliminate 2.  We next use the sum of
the digits test for 9 and 3.  9 is not prime, but since the test is
easy, I always use it if the sum of the digits add to a number
divisible by 9.  The sum of the digits is 12, so 3 is a factor but 9
is not.  

571 x 3 and we then only have to search up to 23 because the truncated
square root of 571 = 23.  

Five won't work by inspection so, what I do is get the handy
calculator and try dividing by 7,11,13,17,19,23.  Only takes a moment.
You find that 571 is prime.  So, the factors of           1713 = 3
x571.  I checked my answer with my 149 dollar TT-89 calculator which
has a factor function.  This calculator is not required in many
college math courses but usually not in high school.

Many text books have divisibility rules for 2, 3, 4, 5, 6, 8, 9 and
11.  It helps to learn these.  

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